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The freezing and melting of $^{4}$He in various aerogels with porositiesranging from 92 to 97% was studied using longitudinal ultrasound. The freezingpressure, detected by a change in velocity and attenuation, was elevated fromthat of bulk by about 0.3 MPa, and showed little dependence on aerogelporosity. We report measurements of the transmission of sound through thesolid-liquid interface in aerogel, for the first time, which was independent oftemperature and unaffected by a small addition of $^3$He, unlike the bulkinterface. This indicates that crystal growth was suppressed by disorder,originating from silica strands. However, small amounts of $^3$He in the solidsignificantly decreased the attenuation, because the resultant pinning ofdislocations by $^3$He suppressed phonon scattering, as is observed in bulksolid $^4$He.

Ultrasound study of the solid-liquid transition and solid-liquid interface of $^4$He in aerogels